## Linear Operators: Spectral theory |

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where ii ( s , t ) } ; ( t ) dt , j = 1 JO | | | | | 2 = SA LAK ( a , b ) | 2v ( da yı ( db ) < the

series converging unconditionally in the topology of Lg . Conversely , if Kij is any

family of

where ii ( s , t ) } ; ( t ) dt , j = 1 JO | | | | | 2 = SA LAK ( a , b ) | 2v ( da yı ( db ) < the

series converging unconditionally in the topology of Lg . Conversely , if Kij is any

family of

**kernels**satisfying ( i ) , . . . , ( iv ) , then ( v ) defines a Hilbert - Schmidt ...Page 1590

For a detailed exposition of the problems connected with the calculation of the

Green ' s

E . Mohr [ 1 ] may be found valuable . Section 4 . The work of Hilbert [ 1 ] in 1904 ...

For a detailed exposition of the problems connected with the calculation of the

Green ' s

**kernel**for a differential operator on a finite interval , the recent paper ofE . Mohr [ 1 ] may be found valuable . Section 4 . The work of Hilbert [ 1 ] in 1904 ...

Page 1624

Let us indicate briefly how the

are known . A formal differentiation gives the following partial differential equation

for K : a K 22K , at2 apz = 9 ( t ) K , ( s , t ) with the boundary conditions K ( t , 0 ) ...

Let us indicate briefly how the

**kernel**K , is obtained once the functions f ( t , 2 )are known . A formal differentiation gives the following partial differential equation

for K : a K 22K , at2 apz = 9 ( t ) K , ( s , t ) with the boundary conditions K ( t , 0 ) ...

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### Contents

IX | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Compact Groups | 945 |

Copyright | |

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additive adjoint operator algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently consider constant contains continuous converges Corollary corresponding defined Definition denote dense derivatives determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero